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GO-spaces with  -closed discrete dense subsets
Author(s):
Harold
R.
Bennett;
Robert
W.
Heath;
David
J.
Lutzer
Journal:
Proc. Amer. Math. Soc.
129
(2001),
931-939.
MSC (1991):
Primary 54F05, 54E35;
Secondary 54D15
Posted:
October 16, 2000
MathSciNet review:
1707135
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Abstract:
In this paper we study the question ``When does a perfect generalized ordered space have a  -closed-discrete dense subset?'' and we characterize such spaces in terms of their subspace structure,  -mappings to metric spaces, and special open covers. We also give a metrization theorem for generalized ordered spaces that have a  -closed-discrete dense set and a weak monotone ortho-base. That metrization theorem cannot be proved in ZFC for perfect GO-spaces because if there is a Souslin line, then there is a non-metrizable, perfect, linearly ordered topological space that has a weak monotone ortho-base.
References:
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Additional Information:
Harold
R.
Bennett
Affiliation:
Department of Mathematics, Texas Tech University, Lubbock, Texas 79409
Robert
W.
Heath
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15213
David
J.
Lutzer
Affiliation:
Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187
Email:
lutzer@math.wm.edu
DOI:
10.1090/S0002-9939-00-05582-9
PII:
S 0002-9939(00)05582-9
Keywords:
Generalized ordered space,
linearly ordered space,
perfect,
$\sigma$-discrete dense subset,
$G_\delta$-diagonal,
metrization,
weak monotone ortho-base,
Souslin line
Received by editor(s):
September 9, 1998
Received by editor(s) in revised form:
June 6, 1999
Posted:
October 16, 2000
Dedicated:
Dedicated to the memory of F. Burton Jones
Communicated by:
Alan Dow
Copyright of article:
Copyright
2000,
American Mathematical Society
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